The polynomial p(x) must have at least two zeros.
A polynomial p(x) can have a maximum, minimum, or neither at any given point. The number of zeros of p(x) is equal to the number of positive and negative changes in the sign of the coefficients of the polynomial.
Since p(1) has a relative maximum at (-20), a relative minimum at (13) and a relative maximum at (57), there must be at least two changes in the sign of the coefficients. Therefore, the polynomial p(x) must have at least two zeros.
To determine how many zeros the polynomial has, we will need to calculate the sign of the coefficients at each point. For example, if the coefficient of x2 is positive at x = -20, but negative at x = 13, then we know that the polynomial has one zero between -20 and 13. We can use this method to determine the number of zeros of p(x).
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Solve the equation 4(2x + 1) = 6x − 12. (1 point)
a. x equals negative thirteen halves
b. x = −8
c. x = 8
d. x equals eleven halves
Answer:
[tex] \sf \: b) \: x = - 8[/tex]
Step-by-step explanation:
Given equation,
→ 4(2x + 1) = 6x - 12
Now the value of x will be,
→ 4(2x + 1) = 6x - 12
→ 8x + 4 = 6x - 12
→ 8x - 6x = -12 - 4
→ 2x = -16
→ x = -16/2
→ [ x = -8 ]
Hence, the value of x is -8.
What is the volume of a rectangular pyramid with a congruent base and the same height?
The volume of a rectangular pyramid with a congruent base and the same height is 1 1/2 cu.in.
In this question we have been given the volume of a rectangular prism which is 4 1/2 cu.in.
We need to find the volume of a rectangular pyramid with a congruent base and the same height.
Volume of rectangular pyramid = 1/3 * length * width * height
And the volume of rectangular prism = length * width * height
So, the relationship between the volumes of the rectangular prism and pyramid which have the same height and base:
Volume of rectangular pyramid = 1/3 * Volume of rectangular prism
In this question we ahve been given volume of a rectangular prism = 4 1/2 cu.in.
First we write improper fraction 4 1/2 as proper fraction.
4 1/2 = 9/2
From above equation,
volume of rectangular pyramid = 1/3 * 9/2
Volume of rectangular pyramid = 3/2
Volume of rectangular pyramid = 1 1/2 cu.in.
Therefore, the volume of a rectangular pyramid = 1 1/2 cu.in.
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The complete question is:
The volume of a rectangular prism is 4 1/2 cu.in. What is the volume of a rectangular pyramid with a congruent base and the same height?
Gabriella needs 120120 meters of fence to surround a rectangular garden. The length of the garden is three times its width, ww. How wide is the fence?.
The rectangular garden's width is 15 units, and Gabriella needs 120 meters of fence to enclose it.
The perimeter of a rectangle is the length of its side boundaries. A rectangle's perimeter is equal to twice the product of its length and width.
[tex]P=2(l+w)[/tex]
In this case, the rectangle's length is (l) and its width is (w).
Assume for a moment that the garden is l units long. The garden is three times longer than it is wide, w. Thus,
[tex]l=3w[/tex]
Gabriella requires 120 meters of fencing to enclose a square garden. The perimeter of the rectangular garden is the same height as this fence. Thus,
[tex]P=2(l+w)\\120=2(l+w)[/tex]
Add this equation with the length value from equation 1.
[tex]120=2(3w+w)\\3w+w=\frac{120}{2} \\4w=60\\w=\frac{60}{4} \\w=15[/tex]
Gabriella needs 120 meters of fence to enclose the rectangular garden, which has a width of 15 units.
The complete question is:-
Gabriella needs 120 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w. How wide is the fence?
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An agent sells life insurance policies to five equally aged, healthy people. According to recent data, the probability of a person living in these conditions for 30 years or more is 2/3. Calculate the probability that after 30 years:
O All five people are still living.
O At least three people are still living.
O Exactly two people are still living.
The number of people still living has a Binomial (n = 5, p = 2/3)
The probability of all five people still living is
P(X = 5) = (2/3)⁵ ≈ 0.1317
The probability of exactly two people living
P(X = 2) = 10 x (2/3)² (1/3)³ ≈ 0.16
The probability of at least three people still living
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)
≈ 0.3292 + 0.3292 + 0.1317
≈ 0.790
Probability is simply the probability that something will happen. Whenever the outcome of an event is uncertain, we can talk about the probability of a particular outcome, i.e. its likelihood. The analysis of events driven by probability is called statistics.
Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes.
Properties:
The probability of an event that cannot happen is either phi or a null set.The total number of possible outcomes in an event's sample space is its maximum probability. Any event has a probability between 0 and 1. A probability of 0 can also exist).An event cannot have a negative probability.The probability of either A or B occurring is equal to the sum of the probability of A and the probability of B if A and B are two outcomes that cannot occur simultaneously.To learn more about Probability:
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Plis bantuin makasih
Answer:
1) (i) dan (iii) karena gradiennya sama "4x"
2) gradien = 1/3
3) gradien = 4/7
4) y = 4/9x - 1/3
5) saya tidak tahu
6) (iii) dan (iv) karena gradiennya sama "3x"
7) y = 3x + 2
8) m = 2 c = -3
9) y = -2/3x + 3
10) g = -4/5
Step-by-step explanation:
1) i) y = 4x +10
ii) y = 2x +3
iii) y = 4x+5
iv) y =-2x +5
(i) dan (iii) karena gradiennya sama "4x"
2) g = (6-0)/(-2-0)
g = 6/-2
g =-3
m1 x m2 = -1
m2 = -1 / (-3)
m2 = 1/3 -----> gradien
3) A(0,0)
Hitung kotaknya
7 -----> Baik
4 -----> ke atas
gradient = 4/7
4) y = mx + c
1 = m(3) - 1/3
1 + (1/3) = m(3)
(4/3) / 3
m = 4/9
y = 4/9x - 1/3
5) saya tidak tahu
6) (iii) dan (iv) karena gradiennya sama "3x"
7) g = (6-3) / (-5-4)
g = -1/3
y - y1 = m (x -x1)
y - (3) = -1/3 (x - 4)
y = -1/3x + 4/3 + 3
y = -1/3x + 13/3
m1 x m2 = -1
m2 = -1 / (-1/3)
m2 = 3
y - y1 = m (x -x1)
y - (-4) = 3 (x - (-2))
y = 3x + 6 - 4
y = 3x + 2
8) g = (1-5) / (2-4)
g = 2
y - y1 = m (x - x1)
y - 5 = m (x - 4)
y = 2x - 8 + 5
y = 2x - 3
m = 2 c = -3
9) -2y = 12 - 3x
y = 3/2x - 6
m1 x m2 = -1
m2 = -1 / (3/2)
m2 = -2/3
y - y1 = m (x - x1)
y - (-1) = -2/3 (x - 6)
y = -2/3x + 4 -1
y = -2/3x + 3
10) g = (-20-0) / ( 0-(-25))
g = -4/5
Saya berharap jawaban saya membantu anda.
Three regular polygons meet at a point
Two of the polygons are pentagons.
Find the number of sides of the third polygon.
You must show your working.
The third polygon must have five sides as well, since the interior angles of the three polygons must add up to 360°.
The interior angle of a regular pentagon is 108°. Therefore, the three pentagons must have a total of 3 x 108° = 324°. The remaining 36° must come from the third polygon, which must also have five sides.
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A local bike shop keeps track of each day's income and expenses using an excel spreadsheet. The sum of all of the transactions was $239.41 on Saturday. Enter an equation that would determine the value of the new mechanic's box (x).
The value of the new mechanic box is $94.96.
What is the value of the new mechanic's box (x)?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the mechanic box be x.
Since the sum of all of the transactions was $239.41 on Saturday, this will be illustrated as:
147.50 + 32.47 + x + 25.32 - 50.64 = 249.41
154.65 + x = 249.41
Collect like terms
x = 249.41 - 154.65
x = 94.96
The mechanic box is $94.96
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The Question is in the picture
The expression for final velocity is; [tex]v_{f}[/tex] = [tex]v_{i}[/tex] + at
Change of subject of formula.
Subject of formula is a topic which involve expressing a variable in terms of other variables in a given mathematical expression.
Acceleration of an object is its change in velocity divided by change in time.
From the given question;
a = [tex]\frac{v_{f} - v_{i} }{t}[/tex]
cross multiply to have
[tex]v_{f}[/tex] - [tex]v_{i}[/tex] = at
So that;
[tex]v_{f}[/tex] = at + [tex]v_{i}[/tex]
= [tex]v_{i}[/tex] + at
Therefore the expression for final velocity in terms of other variables is;
[tex]v_{f}[/tex] = [tex]v_{i}[/tex] + at
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How many solutions does the following equation have ?- 15y 7 17y 2y 70 − 15y 7 17y 2y 70?
There are no potential remedies for -15y + 7 + 17y = 2y + 70.
What is meant by Mathematical equation?An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. After solving this equation, we learn that the value of the variable x is 7.Given,
Unknown to us is that equation.
-15y + 7 + 17y = 2y + 70
The quantity of solutions to the given equation must be determined.
-15y + 7 + 17y = 2y + 70
Modify the terms.
-15y + 17y + = 2y + 70
Conjoin similar terms
2y + 7 = 2y + 70
The equality property of subtraction
2y - 2y = 70 - 7
Conjoin similar terms
0 = 61
However, it is not feasible.
As a result, the provided equation has no solution.
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Do the one you would like please show work
Answer:
8. 12 hours
Step-by-step explanation:
1/6+1/x+1/4
1/x=1/4-1/6
1/x=3/12-2/12
1/x=1/12
x=12
what is 18+15 writen as an expression
find the value of each expression when x=4 and y=5
Answer:
a) 3(4) + 8 = 20
b) 2(4)(5) = 40
c) 6(4+5) = 54
d) (5)² - (4)² = 9
explanation:
change x and y with the value given.
Answer: a.20
b. 40
c.54
d. 9
Step-by-step explanation:
a. 3x4=2+8+20
b.2x4x5=40
c.6x9=54
d.25-16=9
How do you prove a congruence statement?
To prove a congruence statement, you need to demonstrate that two figures are congruent by showing that they have the same size and shape. This can be done by showing that they have the same lengths for corresponding sides and the same measures for corresponding angles. Alternatively, congruence can be proved using transformations, such as translation, rotation, and reflection.
What is an illustration of a congruence statement?For instance, given that ABCDEF, side AB corresponds to side DE because each is made up of the first two letters, side AC corresponds to side DF because each is made up of the first and last letters, and side BC corresponds to side EF because each is made up of the last two letters.
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What will be the end behavior of the graph if the highest degree of the function is odd and its leading coefficient is positive?
The end behavior of the graph will be that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.
The end behavior of a graph is a description of how the graph behaves as the x-values approach either positive or negative infinity. If the highest degree of the function is odd and the leading coefficient is positive, then the end behavior will be that the graph increases without bound as x approaches positive infinity and decreases without bound as x approaches negative infinity. This can be explained by examining the degree of the function. Since the degree is odd, the highest degree of the function must be an odd power, such as x^3. When x is positive and increasing without bound, the value of the function will also be increasing without bound, since the exponent is positive. Similarly, when x is negative and decreasing without bound, the value of the function will also be decreasing without bound, since the exponent is negative.
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How many terms are there in the expression 2x²y * 1 point 1 2 3 4?
The expression 2x²y has in its entirety 1 term.
First let's define what algebraic expressions are.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:
x + y has two termsSince 2x²y has neither addition nor subtraction operations, we can clearly state that it has only one term.
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Pediatricians prescribe 7 milliliters (ml) of acetaminophen for every 35 pounds of a child's weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 55 pounds? The doctor will prescribe *blank* milliliters of acetaminophen.
The number of milliliters of acetaminophen for a 55 kg child is 11 ml
How to find the number of milliliters of acetaminophen the doctor would prescribe?Since a Pediatricians prescribe 7 milliliters (ml) of acetaminophen for every 35 pounds of a child's weight, we desire to find how many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 55 pounds.
First, we need to find the number of milliliters of acetaminophen per pound of child, n
n = number of milliliters, L/mass of child, m
Since
L = 7 milliliters = 7 ml and m = 35 pounds = 35 lbSo, substituting the values of the variables into the equation, we have
n = L/m
= 7 ml/35 lb
= 1/ml/5 lb
= 0.2 ml/lb
Since we require the number of milliters of acetaminophen required for a 55 pound child.
Since n = L/m
L = mn
Given that
m = 55 pounds = 55 lb and n = 0.2 ml/lbSo, susbstituting the values of the variables into the equation, we have
L = mn
= 55 lb × 0.2 ml/lb
= 11 ml
So, the number of milliliters is 11 ml
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What is the real meaning of integral?
An integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
What is integral?This is the value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.
Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation
Integration is used to get the whole by combining combine slices or smaller portions.
Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.
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y varies directly as x. when x = 5, y= 7, what is the value of y if x=10
Answer: y=14
Step-by-step explanation: y is directly proportional to x, meaning that multiplying x by a certain factor would also multiply y by that same factor. x=5 and y=7. If x changes to 10, it means that x is multiplied by a factor of (10/5) = 2. Therefore, y is multiplied by this same factor (2). As a result, 7*2=14
What is the factored form of 3x² 14x 8?
The factored form of 3x² + 14x + 8 is (3x + 4)(x + 2).
What is factor?Factor is a number that can be divided evenly into another number. Factors are used in mathematics to simplify equations, calculate percentages, and solve problems. Factors can also be used to identify the greatest common factor (GCF) between two or more numbers. Factors can also be used to find the least common multiple (LCM) of two or more numbers.
This is the product of the two binomials (3x + 4) and (x + 2),which are the factors of the equation.
The process of factoring an equation involves breaking it down into its component parts,
which in this case are 3x² + 14x + 8. The factors of this equation are determined by first finding the greatest common factor (GCF) of the terms, which in this case is 3x + 4.
Then, the GCF is divided by each of the terms to determine the other factor. For example, 3x² / 3x + 4 =x + 2.
When the two factors are multiplied together, the result is the original equation.
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What are the two different types of values for a parameter Mcq?
The two different types of values for a parameter: Default and user given
The correct answer is an option (2)
In this question we need to select the two different types of values for a parameter.
We know that a parameter is nothing but a special kind of variable which is used in a function to refer to input of the function.
If no argument value is passed during the function call, then the function argument will take default value.
In PL/SQL, user given values for a parameter can be prompted to input a value using & character.
The ACCEPT command is used to obtain input from the user.
Therefore, default value and user given values are two different types of values for a parameter.
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The complete question is:
What are the two different types of values for a parameter?
1) Default and System given
2) Default and user given
3) System given and user given
4) Compile time and run time values
Show that 12 cos 30degrees + 2 tan 60degrees can be written in form roots where k is an integer
The square root of k is 192 which is an integer.
Define Trigonometric functions
A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.
Given expression is,
12 cos 30° + 2 tan 60°
We know,
cos 30° = √3/2
tan 60° = √3
Now, plug in the values
⇒12 * √3/2 + 2 * √3
⇒6√3 + 2√3
⇒8√3
We know, 8 * 8 = 64
The above value in square root form,
⇒√8*8*3
⇒√192
⇒√k (where, k is 192 an integer)
Hence, the square root of k is 192 which is an integer.
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What is the arithmetic mean of the following numbers 8 1 2 6 1 4?
The mean for a given set of observations is 3.67.
What is mean?The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.
Here,
given set of observation,
=1,1,2,4,6,8
=(1+1+2+4+6+8)/6
=3.67
The mean for given set of observation is 3.67.
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What is 5x 2y 3 in slope intercept form?
The line's equation is written as y = (-5/2)x + (3/2) in slope-intercept form.
According to the slope-intercept form, in the equation for a straight line, y=mx+b, the slope is the quantity represented by m that is multiplied on the x, and b is the y-intercept, i.e., the point where the line crosses the vertical y-axis.
To put the equation 5x + 2y = 3 in slope-intercept form, you need to rearrange the equation to have the form y = mx + b, where m is the slope and b is the y-intercept.
To do this, you can start by isolating the y term on one side of the equation:
5x + 2y = 3
2y = -5x + 3
y = (-5/2)x + (3/2)
In this configuration, the line's slope is -5/2, and its y-intercept is 3/2. Therefore, the equation of the line in slope-intercept form is y = (-5/2)x + (3/2).
The complete question is:-
What is 5x + 2y = 3 in slope intercept form?
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What is I3 equal to?
The value of "i" multiplied by the cube is
-i = i³
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i
From this definition, we can know the value of i³, as a multiplication of the following form:
[√(-1)]² = i²
(-1) = i²
i × (-1) = i× i² = i³
-i = i³
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Let f be a differentiable function such that f (2) = 4 and f (2) = − 1/2 . What is the approximation for f (2.1) found by using the line tangent to the graph of f at x = 2 ?
Using line tangent, the approximation for f(2.1) is 3.95
Given,
The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).
The equation be like;
y - f(a) / (x - a) = f'(a)
y = f'(a) (x - a) + f(a)
Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation
y = f'(2) (x - 2) + f(2)
y = -1/2 (x - 2) + 4
To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.
y = -1/2 (x - 2) + 4
y = -1/2 (2.1 - 2) + 4
y = -1/2 x 0.1 + 4
y = 3.95
That is,
The approximation for f(2.1) using line tangent is 3.95
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pls help me
The line 2y + x = 1 is perpendicular to a line L. Line L passes through point (2, -1). Determine the equation of L in the form y = mx + c, where m and c are constants.
The equation of the perpendicular line is y = 2x - 5
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
2y + x = 1
Make y the subject
y = -1/2x + 1/2
Also, from the question;
We have the following points
Point = (2, -1) i.e. (x, y) = (2, -1)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -1/2
This means that the slope is -1/2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 2
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 2
(x₁, y₁) = (2, -1)
So, we have
y = 2(x - 2) - 1
Evaluate
y = 2x - 5
Hence, the line has an equation of y = 2x - 5
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PLEASE HELP!!
Which statement best explains whether △JKL is congruent to △MNP?
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
The statement that best explains whether △JKL is congruent to △MNPis:
"△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin." (Option B).
What is a reflection in Maths?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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I Qule istruction TEAS SmartPrep: Mathematics Posttest An entrepreneur sells of her company to one buyer and to another buyer. What percent of the company does she have left?
The percentage of the company she owns after selling its specific parts is equivalent to 41.66%.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that an entrepreneur sells of 1/2 her company to one buyer and 1/6 to another buyer.
Assume that the amount of company left in percentage is equivalent to {R%}. Let the complete company be represented by 100%. The remaining percent of company after selling half of it can be written as -
100 - {1/2 x 100} = 100 - 50 = 50%.
The remaining percent of company after selling 1/6 of it can be written as -
{R%} = 50 - {1/6 x 50} = 50 - 8.34 = 41.66%
{R%} = 41.66%
Therefore, the percentage of the company she owns after selling its specific parts is equivalent to 41.66%.
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{Complete question is given below -
An entrepreneur sells 1/2 of her company to one buyer and 1/6 to another buyer. What percent of the company does she have left?}
Can someone help me understand this question?
Consider the mathematical sentence 2 ≠ 3.
Is there any variable or constant that you could add to or subtract from both sides, or
multiply or divide both sides by using the Properties of Equality to make both sides equal?
Choose variables and constants to create new mathematical sentences to justify
your conclusion.
Answer:
It is not possible to make both sides of the mathematical equation 2 ≠ 3 equal by using the Properties of Equality. This is because the equation is already in reduced form and there is no way to simplify it further.
If we try to apply the Properties of Equality to this equation, we can see that it is not possible to make both sides equal. For example, if we try to add or subtract a constant or variable to both sides, the result will not be modified. If we try to multiply or divide both sides by a constant or variable, the result will also not be modified.
Therefore, it is not possible to make both sides of the mathematical equation 2 ≠ 3 equal using the Properties of Equality.
Sam is buying packages with 9 beads each. His mom bought him 63 more beads. Now, he has 153 beads. How many packages did he buy? Use algebra to determine the answer.
Answer:
10 packages
Step-by-step explanation:
153-63=90 since each package has 9, 90/9 is 10 packages
the algebraic version is
(153-63)/9=x